Enhancers play a critical role in dynamically regulating spatial-temporal gene expression and establishing cell identity, underscoring the significance of designing them with specific properties for applications in biosynthetic engineering and gene therapy. Despite numerous high-throughput methods facilitating genome-wide enhancer identification, deciphering the sequence determinants of their activity remains challenging. Here, we present the DREAM (DNA cis-Regulatory Elements with controllable Activity design platforM) framework, a novel deep learning-based approach for synthetic enhancer design. Proficient in uncovering subtle and intricate patterns within extensive enhancer screening data, DREAM achieves cutting-edge sequence-based enhancer activity prediction and highlights critical sequence features implicating strong enhancer activity. Leveraging DREAM, we have engineered enhancers that surpass the potency of the strongest enhancer within the Drosophila genome by approximately 3.6-fold. Remarkably, these synthetic enhancers exhibited conserved functionality across species that have diverged more than billion years, indicating that DREAM was able to learn highly conserved enhancer regulatory grammar. Additionally, we designed silencers and cell line-specific enhancers using DREAM, demonstrating its versatility. Overall, our study not only introduces an interpretable approach for enhancer design but also lays out a general framework applicable to the design of other types of cis-regulatory elements.